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Performance of Automatic Active Space Selection for Electronic Excitation Energies

Reza G. Shirazi, Alexander Zech, Peter Pinski, Vladimir V. Rybkin

TL;DR

This work addresses the challenge of automatically constructing balanced active spaces for multireference calculations of electronic excitations. It assesses the Active Space Finder (ASF) workflow, which uses low-accuracy DMRG-CASCI analyses of the two-electron cumulant and one-orbital entropies, starting from MP2 natural orbitals and optionally applying quasi-restricted (QRO) rotations, to select state-averaged active spaces prior to CASSCF/NEVPT2 calculations. The study finds that the best-performing configuration, combining triplet-based initial guesses with QRO and a lowered entropy threshold (l-ASF(QRO)), converges reliably and achieves ≈0.5 eV MAE on a 32-molecule benchmark, though near-degenerate states and too-small spaces remain sources of error. A practical, combined workflow is proposed to address small active spaces, enabling more robust high-throughput excited-state calculations with multireference methods.

Abstract

Computation of electronic spectra is one of the most important applications of methods capturing static electron correlation, including complete-active-space self-consistent field (CASSCF) and post-CASSCF theories. Performance of these techniques critically depends on the active space construction, both in terms of accuracy and computational effort. In this work we benchmark the performance of automatic active space construction, as implemented in the Active Space Finder software, for the computation of electronic excitation energies. The multi-step procedure constructs meaningful molecular orbitals and selects the most suitable active space based on information from more approximate correlated calculations. It aims to tackle a key difficulty in computing excitation energies with CASSCF: choosing active spaces that are balanced for several electronic states. The Active Space Finder is tested with several established data sets of small and medium-sized molecules and shows encouraging results. We evaluate multiple setting configurations and provide practical recommendations.

Performance of Automatic Active Space Selection for Electronic Excitation Energies

TL;DR

This work addresses the challenge of automatically constructing balanced active spaces for multireference calculations of electronic excitations. It assesses the Active Space Finder (ASF) workflow, which uses low-accuracy DMRG-CASCI analyses of the two-electron cumulant and one-orbital entropies, starting from MP2 natural orbitals and optionally applying quasi-restricted (QRO) rotations, to select state-averaged active spaces prior to CASSCF/NEVPT2 calculations. The study finds that the best-performing configuration, combining triplet-based initial guesses with QRO and a lowered entropy threshold (l-ASF(QRO)), converges reliably and achieves ≈0.5 eV MAE on a 32-molecule benchmark, though near-degenerate states and too-small spaces remain sources of error. A practical, combined workflow is proposed to address small active spaces, enabling more robust high-throughput excited-state calculations with multireference methods.

Abstract

Computation of electronic spectra is one of the most important applications of methods capturing static electron correlation, including complete-active-space self-consistent field (CASSCF) and post-CASSCF theories. Performance of these techniques critically depends on the active space construction, both in terms of accuracy and computational effort. In this work we benchmark the performance of automatic active space construction, as implemented in the Active Space Finder software, for the computation of electronic excitation energies. The multi-step procedure constructs meaningful molecular orbitals and selects the most suitable active space based on information from more approximate correlated calculations. It aims to tackle a key difficulty in computing excitation energies with CASSCF: choosing active spaces that are balanced for several electronic states. The Active Space Finder is tested with several established data sets of small and medium-sized molecules and shows encouraging results. We evaluate multiple setting configurations and provide practical recommendations.

Paper Structure

This paper contains 10 sections, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Requirements for automatic active space determination
  4. Algorithm
  5. Details of the ASF Calculation
  6. Computational set-up
  7. Testing data sets
  8. Results and Discussion
  9. Conclusions
  10. Acknowledgements

Figures (2)

  • Figure 1: Mean absolute errors wrt. benchmark excitation energies values for the test data set. Orange - the entire data set of 32 molecules; grey - reduced data set (29 molecules).
  • Figure 2: A combined ASF protocol: one loops over guess orbitals generation methods until the active space has more than three virtual orbitals, which is denoted as min in the diagram. The order of the methods is: 1) QRO, 2) singlet (S) based on their performance. In rare case where both methods suggest a small active space, a QRO guess should be used.